Accurate Two-Phase Flow Simulation in Faulted Reservoirs by Combining Two-Point Flux Approximation and Mimetic Finite Difference Methods

Abstract

Summary Faulted reservoirs are commonly modeled by corner-point grids (CPGs). Because the two-point flux approximation (TPFA) method is not consistent on non-K-orthogonal grids, multi-phase flow simulation using TPFA on CPGs may have significant discretization errors if grids are not K-orthogonal. We developed a novel method to improve the simulation accuracy where the faults are modeled by polyhedral cells, and mimetic finite difference (MFD) methods are used to solve flow equations. We use a cut-cell approach to build the mesh for faulted reservoirs. A regular K-orthogonal grid is first constructed, and then cells are divided where fault planes are present. Most cells remain K-orthogonal while irregular non-K-orthogonal polyhedral cells can be formed with multiple cell divisions. We investigated three spatial discretization methods for solving the pressure equation on general polyhedral grids, including the TPFA, MFD, and TPFA-MFD hybrid methods. In the TPFA-MFD hybrid method, the MFD method is only applied to the part of the domain with severe grid non-K-orthogonality, while the TPFA method is applied to the rest of the domain. We compare flux accuracy between TPFA and MFD methods by solving a single-phase flow problem. The reference solution is obtained on a rectangular grid, while the same problem is solved by TPFA and MFD methods on a grid with non-K-orthogonal cells near a fault. Fluxes computed using TPFA exhibit larger errors in the vicinity of the fault, while fluxes computed using MFD are still as accurate as the reference solution. We also compare saturation accuracy for two-phase (oil and water) flow in faulted reservoirs when the pressure equation is solved by different discretization methods. Compared with the reference saturation solution, saturation exhibits non-physical errors near the fault when the pressure equation is solved by the TPFA method. Because the MFD method yields accurate fluxes over general polyhedral grids, the resulting saturation solutions agree with reference saturation solutions with an enhanced accuracy when the pressure equation is solved by the MFD method. Based on the results of our simulation studies, we observe that the accuracy of the TPFA-MFD hybrid method is very close to the accuracy of the MFD method, while the TPFA-MFD hybrid method is computationally cheaper than the MFD method.